Multi-partite subspaces containing no locally inaccessible information

TL;DR

This paper demonstrates that all measurements on two-dimensional quantum subspaces can be performed locally, revealing a fundamental property of such subspaces with implications for quantum secret sharing and error correction.

Contribution

It proves that any measurement on two-dimensional subspaces in quantum systems can be done locally, regardless of entanglement or multipartite structure, which is a novel fundamental property.

Findings

Two-dimensional subspaces allow only locally accessible measurements.

Any measurement on these subspaces can be performed with local operations and classical communication.

This property has practical implications for quantum secret sharing and error correction.

Abstract

One notion of non-locality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus, contrary to the classical case, there exists information in quantum many body systems which cannot be accessed locally. We show however that, remarkably, two-dimensional subspaces do not have this property: any physically allowed measurement on information encoded in any two-dimensional subspace, regardless of entanglement or multi-partite structure, may be performed locally. Further, this requires only local measurement and feed-forward of classical information, readily achievable in many experimental platforms. As an application to quantum secret sharing we suggest a twist on a well known quantum information splitting protocol, which ensures that no receiving party ever has access to the full state sent, but parties must work together to perform measurements on the state. These results may have practical applications to the measurement of encoded qubits in e.g. quantum secret sharing, quantum error correction, and reveal a fundamental property unique to two-dimensional subspaces.